It really isn't that hard folks.
If you have the name of the child, which you should have if you are going to invite them to a party, then the internet is a wonderful tool. Unless you are open enrolled or at a private school where kids come from all over the place, it is pretty easy to look up a name and address online via websites such as
www.dexknows.com.
Some of us even still get those huge, antiquated things called phonebooks on our doorstep every year where we can actually open them up and look up the name and get the address.
If your child is very young and only wants to invite "Bobby" but you have no idea what their last name is, then ask a good friend's parent (a kid that is going to be invited anyway) what the last name is.
Yes, it takes some time and work, but that is our responsibility as a parent. And it certainly is not rocket science to find out how to invite kids to a birthday party while still being discreet.